C₁₃×#13646 #15699985

order	3328
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#13646

Subgroups

	subgroup	G/H
center	C₂×C₁₃×C₁₆	C₂³
commutator	C₂²	C₂²×C₁₃×C₁₆
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
socle	C₂²×C₁₃	C₂²×C₁₆
prime radical	C₂×D₄×C₁₃	C₁₆
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₁₃×C₁₆ ◁ G

202 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,22,27,23,28,36,43,24,20,29,31,37,32,44,46,21,25,33,38,34,39,47,48,35,30,26,40,41,45,42,49);(15,17)(19,25)(20,30)(27,38)(28,39)(31,40)(32,45)(43,48)(46,49);(18,20,22,31,23,32,36,46,24,25,29,38,37,39,44,48,21,30,33,40,34,45,47,49,35,19,26,27,41,28,42,43)

Conjugacy classes & character table

1456 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6634);